Predicting excretion rates of microzooplankton from carbon metabolism and elemental ratios

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1 468 Comment Limnol. Oceanogr., 38(2), 1993, , by the American Society of Limnology and Oceanography, Inc. Predicting excretion rates of microzooplankton from carbon metabolism and elemental ratios During the past decade, small protozoan consumers of bacteria and phytoplankton at the base of the food web have become well established as dominant nutrient remineralizers in aquatic systems, particularly the open oceans (e.g. Stout 1980; Taylor 1982; Goldman and Caron 1985; Goldman et al. 1985; Andersen et al. 1986). The importance of this role can be attributed in part to the high biomass-specific metabolic rates of these small organisms and to their lower gross growth efficiencies (GGE) relative to bacteria, which were previously assumed to be significant remineralizers (Williams 198 1; Azam et al. 1983). Another factor is diet. Bacterivorous nanoflagellates, in particular, consume prey with C : N ratios (1 : 4) far greater than they need for growth (5 1 : 6); hence, high rates of excretion of excess N are expected. The opposite is true for bacteria and herbivorous mesozooplankton, which, like copepods, typically conserve N because their N : C requirements for growth exceed those available in food (phytoplankton or phytoplankton-derived dissolved and particulate organic matter, DOM and POM). Caron and Goldman ( 1988) and Caron et al. (1990) have advanced the following predictive relationship as a guide to understanding and studying the relationships among nutrient excretion rate, carbon metabolism, and diet of microzooplankton: EN = R, 1 - x KN : C,,,) - x (N : C,,>l (1) where EN and Rc are nutrient (e.g. N) excretion and C respiration rates, is carbon-based gross growth efficiency, and N : Cprey and Accepted: 12 October Acknowledgments This study was supported by NSF grant OCE A contribution from the School of Ocean and Earth Science and Technology, University of Hawaii at Manoa. N : Cpred are nutrient-to-carbon ratios for the prey (food) and the predators (consumers). Although they reported substantial agreement between experimental results and the predictions of this model, their assumption that all ingested C and N is either incorporated into growth or remineralized (i.e. insignificant loss of undigested POM or DOM) may be generally unrealistic for phagotrophic protists. A more general expression for nutrient excretion rate as a function of carbon metabo- lism, growth efficiency, and N : C ratios can be derived from simple elemental budgets assuming that ingested material must be assimilated by the organism before it is used for growth or metabolism. For the element nitrogen EN = AEN X IN - G, (2) where AEN is the assimilation efficiency (as a decimal fraction), IN the ingestion rate, and GN the growth rate in terms of N. A similar expression relates respiration rate (R,) to assimilation efficiency (AE,) and ingestion (Ic) and growth (G,) rates in terms of carbon: Rc = AEc x Ic - Gc. (3) N- and C-based ingestion and growth rates are related by the N : C ratios of the prey and the predator: and Substituting I, = Ic x (N : c,,,) (4) GN = Gc X (N : Cpred). (5) Eq. 4 and 5 into 2 yields EN = AEN X 1, X (N : C,,,) - Gc (N : Cpred)* (6) If we now replace Gc by the definition = I, x GGE,, Eq. 6 becomes EN = AEN X Ic x KN : Cpre,) - Gc AE x (N : C,r.dl. (7) N Finally, to put Eq. 7 in the format that most

2 closely resembles Eq. 1, we must multiply the right side by the identity R&I, x (AE, - GGE,)] from Eq. 3; therefore, AEN x R, EN = (AE, - GGE,) Comment x (N : C,,,) - s 1 x (N: qmd) - N (f-9 The difference between Eq. 1 and 8 is that assimilation efficiencies for both C and N must be known to predict excretion rates. Equation 8 has appeared in various forms in the zooplankton literature for the past 30 yr. Ketchum (1962) was apparently the first to consider the cycling of elements by zooplankton in these terms, and Corner and Davies (197 1) used a similar budgetary approach to speculate about the role of zooplankton in nitrogen and phosphorus cycles in the sea. More recently, Le Borgne (1978, 1982) used the same set of equations to derive an approach for assessing zooplankton secondary production. As observed by Caron et al. (1990), Eq. 1 has also had a history in the literature on bac- terial growth and metabolism (e.g. Fenchel and Blackburn 1979; Blackburn 1983; Lancelot and Billen 1985). In this regard, it is important to note that Eq. 8 reduces to Eq. 1 when AEN = AE, = 1.O, which is typically the case for bacterial osmotrophy in which low-molecularweight molecules are assimilated across the cell wall with no net loss to defecation. Thus, except for the recent studies by Caron and Goldman (1988) and Caron et al. (1990), it would appear that the historical uses of Eq. 1 and 8 have generally been consistent with nutritional modes of the organisms being studied. Using the bacterial model to describe the energetic rate relationships of particle-consuming organisms may introduce errors and biases in predictions. To assess the possible magnitudes and directions of these problems, I examined the behavior of Eq. 8 computationally for combinations of parameters within their expected natural ranges. I varied AE, and AEN in 0.1 increments from 0.7 to 1.O. GGE, was varied from 0.2 to 0.5 in similar steps. Consumer N : C was maintained at the Redfield ratio (N : C,, = 0.15; Redfield et al. 1963) to simulate a constant elemental ratio for z 0) AEN=AEc I 1 I Fig. 1. The effect of equal N and C assimilation efficiencies (AE, = AE,) on the ratio of excretion to respiration (E, : R,) as a function of gross growth efficiency (GGE,). The N : C composition of the consumer, N : Cpred = 0.15 for all cases; N : C,,, varies from 0.09 to 0.15 and Equation 1 predictions are given by the lines AE, = AE, = 1.0. growth similar to that (0.16) observed by Caron et al. (1990). However, the elemental ratio for food was varied from Redfield to levels approximating the natural extremes from bacteria (N : CPre. = 0.25) to N-deficient phytoplankton (N : CPreY = 0.09). Caron et al. (1990) reported N-deficient ratios in the ranges of 0.09-O. 11 for the diatom Phaeodactylum tricornutum and 0.06-O. 13 for the chlorophyte Dunaliella tertiolecta. The high and low values for N : C,, used here are Redfield values multiplied and divided, respectively, by the factor Figure 1 shows the calculated EN : Rc ratio for the three values of N : CPreY and for all cases where AEN = AE,. It is interesting to note, though perhaps intuitively obvious, that EN : R, is a constant (=N : C,,,) for all values of GGE and AE, = AEN when the N: C ratio of the diet is identical to requirements for growth (N : cprey = N: Cpred). Caron and Goldman (1988) reported that the agreement between their measured rates of nutrient excretion and those predicted from measured variables on the right side of Eq. 1 was strongest for nutrient-replete prey, presumably near Redfield el- emental composition and that of the predator Paraphysomonas imperforata. This result is not surprising because accurate predictions do not

3 Comment f 0 g z a 5 w ~ Fig. 2. The effect of unequal N and C assimilation efficiencies on the ratio of excretion to respiration (E, : R,) as a function of gross growth efficiency (GGE,) when N : C ratios of predators and prey are equal (N : C,,, = N : Cprey = 0.15). AE, is constant in all cases (AE, = 0.7). r y z K 2 W hinge on the restrictive assumption that AEN = AE, = 1.O under these circumstances-only that the AE values are approximately equal regardless of their magnitude. Because the ratios of EN : Ro for AEN = AEc = 1.O are those that would be predicted from Eq. 1, the discrepancies between these results and those based on assimilation efficiencies < 1.O in Fig. 1 indicate the magnitude of the error when Eq. 1 is applied inappropriately. Where N : CPrey > N : Cpred, Eq. 1 would tend to underpredict EN. When N : C,, < N : Cpred, Eq. 1 over-predicts the true rate. In both cases, the magnitude of the error is small when GGE, is low and increases nonlinearly with increasing GGE. For N : CPreY = 0.25 and AEN = AE, = 0.7, for instance, Eq. 1 underestimates the prediction of Eq. 8 by 5% at = 0.2 and 30% at = 0.5 (Fig. 1). For N : CPreY = 0.09, Eq. 1 overestimates Eq. 8 predictions by 14% at = 0.2 and 500% at = 0.4. At GGEo = 0.5, Eq. 8 predicts a negative EN : R, while Eq. 1 is positive. Negative predictions for EN would be indicative of an organism s role as a sink rather than the source of dissolved inorganic N. For example, bacteria may compensate for N deficiencies in dissolved organic substrate by competing with phytoplankton for NH,+ (Wheeler and Kirchman 1986), which may or may not be physiologically possible for small phagotrophic flagellates. It would seem unlikely that NH o 3 o 4 Fig. 3. The effect of unequal N and C assimilation efficiencies on the ratio of excretion to respiration (E, : R,) as a function of gross growth efficiency (GGE,) when N : C ratios of predators and prey are unequal. N : C,, = 0.15; N : CpreY = 0.09 and AE, is assumed constant (AE, = 0.7). Predictions of Eq. 1 from Fig. 1-O. availability would be high enough to represent an important source of N for such flagellates while, at the same time, their prey were significantly N-deficient. Under most circumstances, assimilation efficiencies for C and N are not expected to be identical; in general AEN > AE, (Conover and Lalli 1974; Ross 1982; Landry et al. 1984). Figures 2 and 3 examine the effect of unequal assimilation efficiencies on predictions of EN : R, for constant AE, = 0.7 and variable AEN. In contrast to all cases where AEc = AEN, predicted excretion rates for predators consuming prey of similar N : C are highly sensitive to inequalities in assimilation efficiencies (Fig. 2). The relatively modest 0.1 difference between AE, = 0.7 and AEN = 0.8, results in 17 and 33% changes in excretion rates for = 0.2 and 0.5. Excretion rates are more than double those predicted by Eq. 1 for GGE, = 0.5 and all AEN > 0.9. As noted, Eq. 1 only overestimates the excretion rate for N: Cpred = N : c&my when AEN < AEc -an unlikely sce- 0.5

4 Comment 471 nario for most metazooplankton, but it would not be far fetched for the net nutrition of mixotrophic protozoa because C produced photosynthetically would be available, by definition, with AE, = 1.0. Figure 3 demonstrates that inequalities in C and N assimilation efficiencies exacerbate the differences between Eq. 1 and 8 predictions when N : CpreY > N : Cpred, but offset some of these differences when N : CpreY < N : Cpred. For calculations in which N : CpreY = 0.25, for instance, varying the parameters for AE, = AEN = 0.7 (Fig. 1) to AE, = 0.7 and AEN = 0.8 results in almost a fourfold increase (to 19%) in the discrepancy between Eq. 1 and 8 predictions at = 0.2. For = 0.5 the combination of AEc = 0.7, AEN = 0.9 results in a factor of more than two difference in predictions for the two equations. In contrast, for N : CpreY = 0.09 one can see that quite reasonable assumptions for assimilation efficiencies (e.g. AE, = 0.7, AEN = ) could produce relatively close agreement between Eq. 1 and 8 predictions for excretion rates. The previous analysis suggests several reasons why Caron et al. (1990) observed results close (0.98, on average) to those predicted, even though they used Eq. 1. First, net assimilation efficiencies may have approached that (AEN = AEc = 1.O) implicitly assumed in Eq. 1 because the design of the experiments allowed many cycles of reingestion of defecated particles. Alternatively, for nutrient-replete prey, assimilation efficiencies need only have been about equal for nutrient elements and C. When N : Cprey = N : Cpred, there is no energetic incentive to assimilate one element at a higher rate than another. Second, for nutrient-deficient prey, inequities in assimilation efficiencies for nutrient elements and C may have been such that the resulting excretion rates landed fortuitously in the range predicted by Eq. 1 (e.g. Fig. 3). Third, the measurements of GGE by Caron et al. (1990) probably overestimate true growth efficiencies by lo-20%, as they suggest, because reingestion of previously defecated particles is not accounted for. Overestimates of GGE reduce the predicted rate of nutrient excretion from Eq. 1 and hence compensate in part for the lack of information on assimilation efficiencies. If the ultimate aim for generating a mathematical relationship for metabolic rates, growth efficiencies, and elemental compositions is to better understand the mechanisms that link these parameters, then a model developed for osmotrophic bacteria (Eq. 1) should not be used to describe the energetics of phagotrophic microzooplankton. The missing terms, assimilation efficiencies, provide information about digestive physiology that may be an important dimension of an organism s adaptive response to changes in the nutritional quality of its prey. From a practical perspective, measuring assimilation efficiencies of microzooplankton is a major obstacle to using the proper relationship among these parameters (i.e. Eq. 8) predictively. Methods that have been used effectively for mesozooplankton require either quantitative recovery of fecal material or at least effective separation of fecal debris from food particles (e.g. Conover 1966). Neither approach is easily applied to microzooplankton which by and large produce fecal debris of the same size as, or smaller than, the prey they consume (Stoecker 1984). Nonetheless, Caron et al. (1985) were able to determine net assimilation efficiencies for P. imperforata from the residual POM and DOM in long-term grazing experiments. These particulate and dissolved fractions should probably be combined in estimating assimilation efficiencies because phase separation by filtration can be arbitrary for very tiny particles and because much of the DOM may be actual egesta released from feeding vacuoles or diffusive loss and breakdown of defecated particles (e.g. Jumars et al. 1989). Accordingly, the results of Caron et al. (1985) suggest an AE for carbon of -80%. This estimate may be crude, since it does not account for reingestion, but it illustrates that assimilation efficiencies of particle-feeding protists are measurable, significant, and ought to be considered in future energetic studies of these important organisms. Department of Oceanography University of Hawaii at Manoa Honolulu, Hawaii References Michael R. Landry ANDERSEN, 0. K., J. C. GOLDMAN, D. A. CARON, AND M. R. DENIWTT Nutrient cycling in a microflagellate food chain: 3. Phosphorus dynamics. Mar. Ecol. Prog. Ser. 31:

5 472 Comment ~QUVI, F., AND OTHERS The ecological role of wa- KETCHUM, B. H Regeneration of nutrients by zooter-column microbes in the sea. Mar. Ecol. Prog. Ser. plankton. Rapp. P.-V. Reun. Cons. Int. Explor. Mer 10: : BLACKBURN, T. H The microbial nitrogen cycle, LANCELOT, C., AND G. BILLEN Carbon-nitrogen p In W. E. Krumbein [ed.], Microbial geochemistry. Blackwell. relationships in nutrient metabolism of coastal marine ecosystems. Adv. Aquat. Microbial. 3: CARON, D. A., AND J. C. GOLDMAN Dynamics of LANDRY, M. R., R. P. HASSEIT, V. FAGERNESS, J. DOWNS, protistan carbon and nutrient cycling. J. Protozool. AND C. J. L.~RENZEN Effect of food acclima- 35: tion on assimilation efficiency of Calanus pacz$cus K. ANDERSEN, AND M. R. DENNETT. Limnol. Oceanogr. 29: 36 l ss. N&ent cycling in a microflagellate food chain. 2. Population dynamics and carbon cycling. Mar. Ecol. Prog. Ser. 24: , AND M. R. DENNE~ Carbon uti- lizition by the omnivorous flagellate Paraphysomonas imperforata. Limnol. Oceanogr. 35: CONOVER, R. J Assimilation of organic matter by zooplankton. Limnol. Oceanogr. 11: AND C. M. LALLI Feeding and growth in done limacina (Phipps), a pteropod mollusc. 2. Assimilation, metabolism, and growth efficiency. J. Exp. Mar. Biol. Ecol. 16: 13 l-l 54. CORNER, E. D., AND A. G. DAVIES Plankton as a factor in the nitrogen and phosphorus cycles in the sea. Adv. Mar. Biol. 9: 10 l-204. FENCHEL, T., AND T. H. BLACKBURN Bacteria and mineral cycling. Academic. GOLDMAN, J. C., AND D. A. CARON Experimental studies on an omnivorous microflagellate: Implications for grazing and nutrient regeneration in the marine microbial food chain. Deep-Sea Res. 32: K. ANDERSEN, AND M. R. DENNETT. 19 ss. N&ient cycling in a microflagellate food chain: 1. Nitrogen dynamics. Mar. Ecol. Prog. Ser. 24: 23 l JUMARS, P. A., D. L. PENRY, J. A. BAROSS, M. J. PERRY, AND B. W. FROST Closing the microbial loop: Dissolved carbon pathway to heterotrophic bacteria from incomplete ingestion, digestion and absorption in animals. Deep-Sea Res. 36: LE BORGNE, R. P Evaluation de la production secondaire planctonique en milieu odanique par la mkthode des rapports C/N/P. Oceanol. Acta 1: Zooplankton production in the eastern tropical Atlantic Ocean: Net growth efficiency and P: B in terms of carbon, nitrogen, and phosphorus. Limnol. Oceanogr. 27: REDFIELD, A. C., B. H. KETCHUM, AND F. A. RICHARDS The influence oforganisms on the composition of sea-water, p In M. N. Hill [ed.], The sea. V. 2. Interscience. Ross, R. M Energetics of Euphausia padjica. 2. Complete carbon and nitrogen budgets at 8 and 12 C throughout the life span. Mar. Biol. 68: STOECKER, D Particle production by planktonic ciliates. Limnol. Oceanogr. 29: STOUT, J. D The role of protozoa in nutrient cycling and energy flow. Adv. Microbial. Ecol. 4: l- 50. TAYLOR, G. T The role of pelagic heterotrophic protozoa in nutrient cycling: A review. Ann. Inst. Oceanogr. Paris 58(suppl.): WHEELER, P. A., AND D. L. KIRCHMAN Utilization of inorganic and organic nitrogen by bacteria in marine systems. Limnol. Oceanogr. 31: WILLIAMS, P. J. LEB Incorporation of microheterotrophic processes into the classical paradigm of the planktonic food web. Kiel. Meeresforsch. S(supp1.): l-28. Limnol. Oceanogr., 38(2), 1993, , by the American Society of Limnology and Oceanography, Inc. Predicting excretion rates of protozoa: Reply to the comment by Landryl Landry (1993) has proposed an equation relating protozoan respiration rate and nutrient excretion rate that includes terms for protozoan assimilation efficiencies for C and nutrients (his equation 8). He points out that the use of a simpler equation presented by Caron and Goldman (1988, 1990), Caron et al. (1990), Accepted: 27 October and Caron (199 l), which did not consider assimilation efficiencies (equation 1: Landry 1993) may result in significant under- or overestimations of nutrient excretion. We agree with the intent and conclusion of Landry s emendation to equation 1. He has clearly and convincingly demonstrated the importance of including assimilation efficiencies in these calculations. If one cannot discount the excretion of organic material in the mass